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# Counter braids: a novel counter architecture for per-flow measurement

Sigmetrics Performance Evaluation Review, no. 1 (2008): 121-132

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Abstract

Fine-grained network measurement requires routers and switches to update large arrays of counters at very high link speed (e.g. 40 Gbps). A naive algorithm needs an infeasible amount of SRAM to store both the counters and a flow-to-counter association rule, so that arriving packets can update corresponding counters at link speed. This has...More

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Introduction

- There is an increasing need for fine-grained network measurement to aid the management of large networks [14].
- Measuring flows with a specific flow 5-tuple in the packet header gives more detailed information such as routing distribution and types of traffic in the network.
- Such information can help greatly with traffic engineering and bandwidth provisioning.
- Measuring such flows is useful during and after an attack for anomaly detection and network forensics

Highlights

- There is an increasing need for fine-grained network measurement to aid the management of large networks [14]
- We have proved in [17] that Counter Braids (CB), with an optimal decoder, has an asymptotic compression rate matching the information theoretic limit
- We evaluate the performance of Counter Braids using both randomly generated traces and real Internet traces
- The reconstruction error Perr is the total number of errors divided by the total number of flows, and the average error magnitude Em measures how big the deviation from the actual flow size is provided an error has occurred
- We presented Counter Braids, a efficient minimum-space counter architecture, that solves large-scale network measurement problems such as per-flow and per-prefix counting
- We mention two: (i) Since a flow passes through multiple routers, and since our algorithm is amenable to a distributed implementation, it will save counter space dramatically to combine the counts collected at different routers. (ii) Since our algorithm “degrades gracefully,” in the sense that if the amount of space is less than the required amount, we can still recover many flows accurately and have errors of known size on a few, it is worth studying the graceful degradation formally as a “lossy compression” problem

Methods

- Corresponding to the goals, we (i) use a small number of hash functions, (ii) braid the counters, and (iii) use a linear-complexity message-passing algorithm to reconstruct flow sizes.
- Performance measures: (1) Space: measured in number of bits per flow occupied by counters.
- The authors denote it by r Note that the number of counters is not the correct measure of compression rate; rather, it is the number of bits.
- The author is the indicator function, which returns 1 if the expression in the bracket is true and 0 otherwise
- The authors chose this metric since the authors want exact reconstruction

Results

- The authors evaluate the performance of Counter Braids using both randomly generated traces and real Internet traces.

In Section 7.1 the authors generate a random graph and a random set of flow sizes for each run of experiment. - The authors use n = 1000 and are able to average the reconstruction error, Perr, and the average error magnitude, Em, over enough rounds so that their standard deviation is less than 1/10 of their magnitude.
- In Section 7.2 the authors use 5-minute segments of two one-hour contiguous Internet traces and generate a random graph for each segment.
- The reconstruction error Perr is the total number of errors divided by the total number of flows, and the average error magnitude Em measures how big the deviation from the actual flow size is provided an error has occurred

Conclusion

**CONCLUSION AND FURTHER WORK**

The authors presented Counter Braids, a efficient minimum-space counter architecture, that solves large-scale network measurement problems such as per-flow and per-prefix counting.- Counter Braids incrementally compresses the flow sizes as it counts and the message passing reconstruction algorithm recovers flow sizes almost perfectly.
- The authors minimize counter space with incremental compression, and solve the flow-tocounter association problem using random graphs.
- (ii) Since the algorithm “degrades gracefully,” in the sense that if the amount of space is less than the required amount, the authors can still recover many flows accurately and have errors of known size on a few, it is worth studying the graceful degradation formally as a “lossy compression” problem
- The authors mention two: (i) Since a flow passes through multiple routers, and since the algorithm is amenable to a distributed implementation, it will save counter space dramatically to combine the counts collected at different routers. (ii) Since the algorithm “degrades gracefully,” in the sense that if the amount of space is less than the required amount, the authors can still recover many flows accurately and have errors of known size on a few, it is worth studying the graceful degradation formally as a “lossy compression” problem

- Table1: Flow estimates at each iteration. All messages converge after Iteration 3
- Table2: Single-layer rate for 2 ≤ k ≤ 7. P(fi > x) = x−1.5
- Table3: Simulation results of counting 2 traces in 5minute segments, on a fixed-size CB with total space B

Funding

- This work has been supported in part by NSF Grant Number 0653876, for which we are thankful
- We also thank the Clean Slate Program at Stanford University, and the Stanford Graduate Fellowship program for supporting part of this work

Reference

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- 2. It has P Write decreasing digit entropy. fi in its q-ary expansion

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